Spiral arm structures seen in scattered-light observations of protoplanetary disks can potentially serve as signposts of planetary companions. They can also lend unique insights into disk masses, which are critical in setting the mass budget for planet formation but are difficult to determine directly. A surprisingly high fraction of disks that have been well studied in scattered light have spiral arms of some kind (8/29), as do a high fraction (6/11) of well-studied Herbig intermediate-mass stars (i.e., Herbig stars >1.5 M ). Here we explore the origin of spiral arms in Herbig systems by studying their occurrence rates, disk properties, and stellar accretion rates. We find that two-arm spirals are more common in disks surrounding Herbig intermediate-mass stars than are directly imaged giant planet companions to mature A and B stars. If two-arm spirals are produced by such giant planets, this discrepancy suggests that giant planets are much fainter than predicted by hot-start models. In addition, the high stellar accretion rates of Herbig stars, if sustained over a reasonable fraction of their lifetimes, suggest that disk masses are much larger than inferred from their submillimeter continuum emission. As a result, gravitational instability is a possible explanation for multiarm spirals. Future observations can lend insights into the issues raised here.